and to Lhe difficulty of following a demonstration without some actual construction, we habitually represent points by dots, lines by thin strokes, and surfaces by thin laminae, and are thereby subjected to the insidious danger of regarding these representa- tions as at any rate approximations to mathematical abstractions, and if we argue from constructions yather than from definitions, we may easily make false assumptions without knowing it. There is no safe receipt for avoiding this danger, but the test of divisibility is an mvaluable check. An assumption is convictably false if it implies that a magnitude is of a different order of diyisibility from that which defines it. But many false assumptions pass un- convicted through want of real grasp of Aristotle’s teaching in this matter.
Measurement. — Yor purposes of measurement and comparison it is convenient to divide up quanta into standard units, and to express them as aggregates of these units.
A ‘unit’ is not a ‘ unity’ in the sense of being indivisible, for it may be either an individual, or a group, or a magnitude, or anything else which for the purpose of manipulation, measurement, and com- parison il is convenient Lo treat as a single whole. Any unit suitable for the purpose in hand may be taken as the standard unit, and different units will be required according to the quanta and the conditions to be dealt with.
Sometimes the unit will be a specific magnitude, such as a yard, a ton, a load or a cupful; sometimes it will be a kind of individual irrespective of mag- nitude, such as a inan or a chair; or it may be a group of individuals, such as a coustellation of stars lxxxv INTRODUCTION or a grove of trees; or again it may be such a thing as a dream, or a taste. It may in fact be anything which can be counted, Units can of course only measure quanta of their own kind: units-of-length measure lengths, units-of- time measure time. An aggregate of units-of-weight is itself a weight, an aggregate of units-of-length is itself a length.
The immaterial ‘ boundaries’ which tell off the successive aggregates are Lheir ‘numbers,’ and the aggregates themselves are named after their specific numbers; so that a given number stands both for a numerating boundary and a numeral aggregate.
The system of aggregation applies to units gua units, not qua parts of specific quanta, and the science of arithmetic depends on the system of aggregation, and is appheable to aggregates of any kind of unit. It is not therefore necessary to specify the nature of the unit in order to investigate the properties of numbers, and when this principle has been grasped il becomes possible to experiment with aggregates of easily accessible units, and to apply the conclusions to those not susceptible of direct manipulation. Thus having discovered expermentally that an aggregate of three pebbles and an aggregate of four pebbles together make an aggregate of seven pebbles, we can deduce the fact that three men and four men make seven men; three hours and four hours make seven hours; three dreams and four dreams make seven dreams, and in general, that three and four units together make seven units.
But if we want to measure specific quanta we must choose specific units. If we are told that a distance is ‘ three ’ we do not know how long it is, but if we lxxxvi INTRODUCTION are told that it is three feet or three inches we do know. If we are told that a weight is ‘ three’ we do not know how heavy it is, but if we are told that it is three pounds we do.
The question now arises of the measurability of a given continuum by a given unit. A unit which null measure the continuum can of course be found, by dividing the continuum itself into equal parts and taking these parts as units. The continuum will then contaitu an exact number of the chosen units. But can we expect that any unit will be an exact fit, if it has been chosen without reference to the con- tinuum to be measured ἢ Take, for instance, a length OA and measure off successive units on the same line.
If one of the boundaries which mark off the successive units coincides with the point A which marks the end of the line OA (as in Fig. 1), then the unit will be an exact measure of OA and OA will contain an exact number of these units. But if the point A falls between two successive boundaries (as in Fig. 2), then the unit is not an exact measure of OA; OA exceeds one number of units and falls short of the next.
Now it would appear at first sight that we could be sure of an exact fit by taking a small enough unit, for the smaller the unit the greater is the number of boundaries in a given space. But small- Ixxx vii INTRODUCTION ness alone gives no ground for the presumption that the fit will be exact. For however numerous the boundaries may be, they must always be ‘ spaced,’ and the point A may fall between two consecutive ones, We cannot prevent this from happening by inserting still more boundaries, for however close these may be, there will always be some interval between them, and as long as there is any interval the point A may fall within it, and then the unit is not an exact measure of the line.
The measurability of a given line by a chosen unit, then, depends not on whether the unit 3 large or small, but on an exact adjustment which is a pure accident, in Aristotle’s sense of this word, unless it has been secured by constructing the unit from the line itself. As there are endless ways of dividing a line into equal parts, so there are endless possible units which exactly measure it, but this does not prevent there being endless possible units which do not exactly measure it.
When two lines can both be measured exactly by the same unit they are said to be commensurable.
We cannot assume that any two lines OA and OB taken at random will be commensurable, for there is no ground for supposing that any unit constructed from OA (by dividing OA into equal parts) will be an exact measure of OB, or that a unit constructed from OB will be an exact measure of OA.
When the ratio (.e. relation of magnitude) of two lines is such that they cannot be measured exactly by the same unit they are said to be incommensurable. But this does not imply any vagueness or instability in their relationship, but simply that it cannot be expressed numerically, for the lines are not both lyxxvili INTRODUCTION aggregates of the same umt We are constantly deal- ing with ratios that are neither vague nor unstable though they are incommensurable. Tor instance, the ratio of the side of a square to its diagonal is in- commensurable, and so is the ratio of the cireumfer- ence of a circle to its diameter.* Infinity. —No actual quantum and no actual process can be unlimited, but a process may be potentially unlimited. An actual quantum may be subject to a potentially unlimited process (such as subdivision), but this does not endow the quantum itself with the quality of potential unlimitedness, for it is in virtue of continurty not of size that the process of subdividing is limitless. just as a long line is potentially divisible into any number of equal parts, so is a short one, for the ‘boundaries’ which divide it take up no room, and therefore do not tend to exhaust the short line any more than the long one.
But as the line is neither increased nor diminished by being divided up, it follows that in a given line the length of its parts must vary with their number, and as the number increases the length must diminish, Thus the processes of numeration and diminution keep pace with that of subdivision. And as there is no limit to potential subdivision, neither can there be any limit to potential numeration and diminution. But these unlimited potentialities cannot be transmuted into “ The atomists contended that all quanta were reducible to indivisible particles or ‘ monads,’ and that these con- stituted the ultimate units from which all quanta are built up. In their view, therefore, all ratios were conimensurable.
Aristotle, on the other hand, held that there was no limit to the potential divisbility of a continuum. In his view, therefore, there would be no ‘ ultimate units’ of a continuum, and therefore there nust be mcommensurable ratios.
lxxxix INTRODUCTION unlimited actualities, for however far the process of subdivision is carried it must actually stop some- where, and is therefore limited; the result will be an actual nuniber of actual parts; but no actual number ig unlimited, and the limitation of the number of the parts automatically hmits their diminution.
Actually, then, all these processes — division, numeration, und diminution—are limited. In fact. no actuality can be unlimited, for aetualization means achievement, and imagmation can always stretch be- yond achievement; απ the unlinnted potentialities will always remain beyond the limited actualities, Unlimitedness then exists, nut as an accomplished fact, but as an open possibility which cannot be closed. ΤῈ is unachievable, and exists only in virtue of being unachievable.
xe ARISTOTLE’S PHYSICS VOL. I B BOOK I INTRODUCTION A vavounrre method of Aristotle’s, in investigating any subject, is to begin by surveying the opinions of previous thinkers (or, in lack of such, the cwrent opinions and usages of speech) and endeavouring tu discover some common trend in which they agree, perhaps even when they suppose themselves to be in flat contradiction. If he succeeds so far, he endeayours to define the direction of this common trend, to push it forward to its natural goal, and there to formulate it. If the result so reached enables him to reveal some aspect or fragment of truth underlying each thinker’s system, and at the same time to show why his imperfect formulating of it exposed him to error, we may then feel that we have a reasonable guarantee of ils soundness.
This is the method pursued in Book I., but it seems, at first sight, to bring us in a very slender harvest; for at the end of a discussion which puts a very severe strain upon our attention we find ourselves rewarded by nothing more startling than the assurance that some changes are possible and others not, and that, where there is any change at all, there is something that undergoes the change and some change that it undergoes, so that something is there at the end that was not there at the beginning. A good deal of trouble is spent in considering how to formu- late this statement most effectively, but the statement itself appears not only to be vbvious but to be irrelevant to the questions with which the Book opens, and as to 8 ARISTOTLE which the opinions of the earlier thinkers are collected; for we begin by asking, out of how many elemental bodies the world of Nature is physically compounded, and we end by trying to determine into haw many factors it is conceptually convenient to resolve the process of ‘ changing.’
This is all so, and Aristotle will deliberately have it go. But all the saine this Book is a very serious piece of work and in its way a model of discussion. A short introductory chapter gives us the key, if we can but find the skill to turn it through the wards.
In this chapter Aristotle lays it down that investigation should begin at the beginning and make for the end, which means beginning where we are and making for where we want to be, and this again (in the case of Nature at any rate) means heginning with the concrete and chang- ing phenomena of the world revealed to the senses, and making for abstract and stable theoretical generalizations that will introduce order, connexion, and sequence into our intellectual apprebension of them; in a word, our progress must be from the phenomena accessible to the senses to the conceptions that satisfy the intelligence.
Now, according to Aristotle, all his precursors took the opposite course. They began by laying down a general proposition that satisfied, or was even demanded by, their intelligence, and then tried to arrange the facts in harmony with it. The consequence was that their startingoint had no firm attachments to the real subject of investigation, and their deductions led them to more or less unfruitful and insecure results. But no one knows better than Aristotle that it is balf the battle to know what you want to get at and to ‘ ask the right questions’ about it; and it will therefore be a good day’s work if he can show his readers that, in so far ag his precursors began at the wrong end and were true to their own method, they disagreed with each other and arrived at comparatively little of primary value; but in so far as they allowed Nature herself to foree them, surreptitiously as it were, to follow the true method, they all manifest a common 4: PHYSICS, I. INTRODUCTION trend and are found to be groping for the right question, which emerges at the end of the Book, instead of the wrong one, suggested by their own axioms, which meets us at the beginning.
Perhaps it may be well at this point to introduce parenthetically a few illustrations, from oar own circle of familiar ideas, of the way in which an accepted ‘ axiom’ of reason may entangle thought and perplex observatiou.
The conception that a thing cannot act and produce an effect except where it is (i.e. the denial of the possibility of actio in distans) has led to dissatisfaction with the law, or even the observed fact, of gravitation, because the statement of it treaty dislant bodies as affecting each other. ‘The same conception has also led to the hy pothesis of a luminiferous ether, the existence of which has obstin- ately evaded all tests, and the constitution of which defies consistent formulation, Or again, Jevons, in his attempt to unify the principles of science, was long baffed hy finding that, whereas in arithmetic one and one make two, in logic one and one make one. At last he discovered that in arithmetic too one and one make one if they are both the same one, It is one and another that make two.
Compare Bergson’s assertion: that the axiom ‘two bodies cannot occupy the saine space’ is contradicted by science all along the line, but still holds its own, because, though not a property of matter, it is a property of two-ness.
These latter examples will serve to illustrate the further point (of great significance in connexion with Aristotle’s refutations) that any speculative axiom we jump at has to be expressed in langnage; and language—which has been evolved by processes that are anything but rigidly logical, systematic, and consistent—embodies many ambiguities and concealy many obscurities; so that, if apparently axiomatic statements are suddenly arrested and petrified, without adequate scrutiny and analysis, the deductions drawn from them may lead us far ταδοο astray.
To return to Aristotle. The particular axiom which he believes to have misled and enslaved his precursors is 5 ARISTOTLE variously expressed as ‘ nothing can come out of nothing or ‘ the existent cannot come out of the non-existent, or the non-existent out of the existent.’ This axiom, ag under- stood by those who accepted it, Aristotle regards as false, The deductions they made from it, so far as they were seriously accepted, Hatly contradicted Nature, and also led to internally self-contradictory conclusions; or at the very least, tended to divert attention from the true problem and from fruitful attempts to deal with it.
Parmenides and his disciples, according to Aristotle, clearly saw that their axiom amounted to a blank con- tradiclion of all change and movement, and so to ἃ con- ception of Nature as unitary and rigidly unchanging and undifferentiated. They granted that ‘appearances’ con- tradict this; that is so much the worse for the appearances, They contradict the truth and therefore do not exist at all, but only ‘ appear’ to do so.
Othera were less consistent, but as they too held it to be impossible for anything to come out of nothing, the ques- tion that chiefly interested them was not ‘ How are we to regard change, and how investigate changes?’ but ‘ What are we to suppose it 19 that is always there in reality, while it appears as if everything were passing in and out of existence?’ It is really all air, said one; all water, said another; the four elements, said a third; every known substance or tissue out of which things are visibly built up by addition and interlacing, said another. Thus they were all of them looking for the ‘ existent,’ i.c. the reality (as distinct from appearance) which never comes to be or ceases to be, but is ‘ always there.’ This, however, was not examining the fact of change (which is the distinctive characteristic of what we mean by Nature) at all. It simply diverted the mind from it. And, obscurely feeling this in spite of themselves, all the thinkers (even including Parmenides himself, when he deigns to look at ‘ appear- ances ’) had recourse to certain agents of change, which they brought in under the guise of ‘ contrasted principles,’ such as ‘hot and cold,’ or ‘more and less,’ and so forth, between which, as between two poles, change takes place 6 PHYSICS, I. INTRODUCTION or seems to do so. Obviously, then, it is here that we must look for the tracks of that driving force of the truth that secretly diverted them from the lines they were trying to follow, and Inred them into an Dalek accord with Nature, and so with each other, even where they were most conscious of mutual opposition.
Thus at last we come to the right questions, and ask: What conceptual analysis of the observed process of change will give us the best starting-point for clear thinking and fruitful observation ὃ What und how many are the factors or constituents of change? What technical terms give best promise of precision and accuracy ἢ Aristotle tries a variety of formulae and compares their merits, always keeping steadily in view the passage of the changing thing from one state to another. He notes @ certain goalfulness in Nature, analogous to our own purposeful actions. Te sees that, 1f we follow any definite series of changes, such as that from the acorn to the oak, we find that at every stage of progress the changing thing lacks something of the thing it is to be, and this‘ shortage ’ is an essential characteristic of what, at the moment, 1t already is: and this provokes interesting reflections as to the elation of the ‘ existent or non-existent ’ philosophy to these ‘ absences’ or ‘shortages,’ which aie negative yet definite. Are they existent or non-existent ἢ What is this ‘not-yel-there-ness’ (which, under a more positive aspect, we call a ‘potentiality ) that goes shares with ‘ already- there-ness’ in the ceaseless ‘ hecomings’ of Nature?
APISTOTEAOYTS ®YSIKH> A CHAPTER I ARGUMENT By ‘understanding’ things we mean getting at their causes and constituent elements, and apprehending first principles. In the order of nature we think of things being built up from their elements, of effects following causes, and of movements and changes as obeying principles But our experience, on the other hand, introduces us first and inost directly to concrete and individual objects and their behanour, and we have to work back from them to general principles or ultimate elements. Our progress, then, in studying nature, must be from what is familiar to our senses to what ts dwminous to our intelligence, or from what is first or most accessible to us, to what is first ov most fundamental in nature (a 16-26).
Names and defimtions are related to synthetic and analytic concepts respectiwely (a 26~b 14). (Aristotle uses ἃ single word (γνώριμον) alike for what can be directly re- cognized by the senses as fact, and for what ix demanded or accepted by the mind as lying behind it and explaining it. The translation makes no attempt to follow him in this.)
[This prefatory chapter is to ‘ clear wp the question of the beginnings of the science of Nature’ (2. 15). The term ‘ beginnings’ (ἀρχαί) ts loosely used without clearly dis- 8 ARISTOTLE’S PHYSICS BOOK I CHAPTER I ARGUMENT (continued) tinguishing three senses: (a) the primary elements of natural things (ὅθεν πρῶτον γίγνεται ἐνυπάρχοντος, Met. 1013 a 4); (5) the starting-points of a science. Jn a systematic science, e.g. geometry, these are (i) the premisses or basic truths (ὅθεν γνωστὰν τὸ πρᾶγμα πρῶτον, 1013 a 14), which are ‘ true, primary, immediate, and intrinsically more intelligible than the conclusion and prior to it, and are apprehended hy intuition (νοῦς). Anal. Post. 71 b 20, 100 b 12. (ii) But the best starting-point for inquiry or learning (μαθήσεως οὐκ ἀπὸ τοῦ πρώτου καὶ τῆς τοῦ πράγματος ἀρχῆς ἐνίοτε ἀρκτέον, ἀλλ᾽ ὅθεν ῥᾷστ' ἂν μάθοι, 1013 a 2) must be‘ things more immediately cognizable to us’ by sense- perception.
The path tu knowledge starts from (a ii) the indistinct (συγκεχυμένον, cf. Poet. 1450 b 37) unanalysed whole (ὅλον) given by sense-perception, which has for its object the concrete individual thing (a man), but dimly discerns in this the universal (Man), Anal. Post. 100 4 16. The analysis of this universal into its constituent parts (μέρη, τὰ καθ᾽ Exagra) carries us up towards the primary concepts and basic truths (Bi), just as we understand the nature of a complex thing when we have analysed it into its elemente (A).
This might lead us to expect that Aristotle would go on to establish, by induction from the data of sense-observation Ὁ ARISTOTLE ARGUMENT (continded) ( ii), the premisses or basic truths (Bi) of Physics. But the ἀρχαί which he proceeds to discuss in Chapter IT. are not sense-data, but the alleged elements of natural things (a). The connexion between the chapters may le in the un- 184219 Βπειδὴ τὸ εἰδέναι καὶ τὸ ἐπίστασθαι συμβαίνει, περὶ πάσας τὰς μεθόδους ὧν εἰσιν ἀρχαὶ ἢ αὕτια ἢ στοιχεῖα, ἐκ τοῦ ταῦτα γνωρίζειν---τότε γὰρ οἰόμεθα γινώσκειν, ἕκαστον, ὅταν τὰ αἴτια γνωρίσωμεν τὰ πρῶτα καὶ τὰς ἀρχὰς τὰς πρώτας καὶ μέχρι τῶν 15 στοιχείων---, δῆλον ὅτι καὶτῆς περὶ φύσεως ἐπιστήμης πειρατέον διορίσασθαι πρῶτον τὰ περὶ τὰς ἀρχάς.
Πέφυκε δὲ ἐκ τῶν γνωριμωτέρων ἡμῖν ἡ ὁδὸς καὶ σαφεστέρων ἐπὶ τὰ σαφέστερα τῇ φύσει καὶ γνωριμώτερα: οὐ γὰρ ταὐτὰ ἡμῖν τε γνώριμα καὶ ἁπλῶς. διόπερ ἀνάγκη τὸν τρόπον τοῦτον προ- 0 ἄγειν ἐκ τῶν ἀσαφεστέρων μὲν τῇ φύσει ἡμῖν δὲ σαφέστερων ἐπὶ τὰ σαφέστερα τῇ φύσει καὶ γνωριμώτερα.
Ἔστι δ᾽ ἡμῖν πρῶτον δῆλα καὶ σαφῆ τὰ συγ- κεχυμένα μᾶλλον: ὕστερον δ᾽ ἐκ τούτων γίνεται γνώριμα τὰ στοιχεῖα καὶ αἱ ἀρχαὶ διαιροῦσι ταῦτα. διὸ ἐκ τῶν καθόλου ἐπὶ τὰ καθ᾽ ἕκαστα δεῖ προ- , Δ A A A εἶ μ᾿ οὖ ἐέναι" τὸ γὰρ ὅλον κατὰ τὴν αἴσθησιν γνωρι- Ἐπ’ 4 καθόλου and καθ᾽ ἕκαστα, when contrasted, usually mean ‘general’ and ‘ particular’; but here they are used in the other and less frequent sense of ‘concrete whole’ and ‘constituent factors’; ag in De gen. et cor. ii. 4 (331 a 20), where ‘ air,’ ‘ water,’ etc., are regarded as each of them constituting a single πᾶν or καθόλου, and their attributes ‘moist,’ ‘ warm,’ etc., as each constituting a καθ᾽ ἕκαστον. Were the words taken in their more usual sense there would not only be an insuperable difficulty here, but also a flat contradiction between this passage and the τὸ μὲν γὰρ 10 PHYSICS, I. τ.
ARGUMENT (continued ) expressed thought that the starting-point (u ii) of our present inquiry must he the confused notions of our predecessors about (a), which we proceed to analyse, with a view to arriving at the true fundamental notions.—C.]} In all sciences that are concerned with principles or causes or elements, it is acquaintance with these that constitutes knowledge or understanding. For we conceive ourselves to know about a thing when we are acquainted with its ultimate causes and first principles, and have got down to its elements. Obviously, then, in the study of Nature too, our first object must be to establish principles.
Now the path of investigation must lie from what is more immediately cognizable and clear to us, to what is clearer and more intimately cognizable in its own nature; for it is not the same thing to be directly accessible to our cognition and to be in- trinsically intelligible. Hence, in advancing to that which is intrinsically more luminous and by its nature accessible to deeper knowledge, we must needs start from what is more immediately within our cognition, though in its own nature less fully accessible to understanding.
Now the things most obvious and immediately cognizable by us are concrete and particular, rather than abstract and general; whereas elements and principles are only accessible to us afterwards, as derived from the concrete data when we have analysed them. So we must advance from the concrete whole to the several constituents which it embraces; α for it is the concrete whole that is the καθόλου κατὰ τὸν λόγον γνώριμον, Td δὲ καθ᾽ ἕκαστον κατὰ τὴν αἴσθησιν, of chap. v. (189 a 5 944. and 72 a 1 sqq.).
11 ARISTOTLE μώτερον, τὸ δὲ καθόλου ὅλον τί éotw: πολλὰ γὰρ περιλαμβάνει ὥσπερ μέρη τὸ καθόλου.
Ilérovbe δὲ ταὐτὸ τοῦτο τρόπον τινὰ καὶ τὰ ὀνόματα πρὸς τὸν λόγον" ὅλον γάρ τι καὶ ἀδιορίστως σημαίνει (οἷον 6 κύκλος), ὁ δὲ ὁρισμὸς αὐτοῦ διαιρεῖ εἰς τὰ καθ᾽ ἕκαστα. καὶ τὰ παιδία τὸ μὲν πρῶτον προσαγορεύει πάντας τοὺς ἄνδρας πατέρας καὶ μητέρας τὰς γυναῖκας, ὕστερον δὲ διορίζει τούτων ἑκάτερον.
CHAPTER II ARGUMENT How many primary constituents of things are there? A few shale or principles, or infinity of atoms? (184 b The dogma, of Parmenides that all Nature is one and rigid, amounts to a dental that any science of ‘ changing material things’ (which is what we mean by Nature) can east at all; and therefore the descussion of it belongs to First Philosophy, not to Physics. Nevertheless, since it has a philosophical interest, and incidentally raises questions that concern the Physicist, we will not stand on our right to ignore it (Ὁ 25- To begin with, then (since there are different ways of ‘ existing’), does the assertion ‘ everything that exists is one’ refer ta substantive, or quaniitive, or qualitive exist- ence? If to all, or to more than one of them, then there ig more than one ‘ existence, and Parmenides 1s wrong. If only to one, then that one must be substantive; for the other categories exist only in relation to the substantively ewistent, But to say either with Mehssus that the existent 18 unlimited, or with Parmenides that it is limited, is to make it quantitive as well as substantive (a 20-b ὃ).
more readily cognizable by the senses. And by calling the concrete a ‘whole’ I mean that it em- braces in a single complex a diversily of con- stituent elements, factors, or properties.
The relation of names to definitions will throw some light on this point; for the name gives an unanalysed indication of the thing (‘circle,’ for imstance), but the definition analyses out some characteristic property or properties. A variant of the same thing may be noted in children, who begin by calling every man ‘father’ and every woman ‘mother,’ till they learn to sever out the special relation to which the terms properly apply.
CHAPTER II ARGUMENT (continued) Again, ‘ one’ is just as ambiguous as ‘ existent.’ It has three meanings: (1) a continuous line may be one, though divisible infinitely; (2) there may be two names for one thing; (8) or an individual (1.6. an ‘ individable’ unit) that ceases to exist as a unit when broken up, may be one. But in none of these senses can ‘ everything’ be ‘ one’ Some later thinkers also—not understanding that the conerete oneness of a single subject may embrace a multitude of attributes and relations, and also believing (through Sailure to distinguish between the copula and the verb sub- stantive) that to say ‘a man. is pale-complexioned’ would imply that ‘ pale-complexioned’ existed as an entity— wrenched language in a vain attempt to avoid the (really quite unimpeachable) attribution af unity and multiplicity to one and the same subject (b 25-186 a 3), 13 20 ARISTOTLE 13 20 ARISTOTLE ᾿Ανάγκη δ᾽ ἤτοι μίαν εἶναι τὴν ἀρχὴν ἢ πλείους" καὶ εἰ μίαν, ἤτοι ἀκίνητον (ὡς φησι ἸΤαρμενίδης καὶ Μέλισοος) 7) κινουμένην (ὥσπερ οἱ φυσικοί, οἱ μὲν ἀέρα φάσκοντες εἶναι οἱ δ᾽ ὕδωρ τὴν πρώτην ἀρχήν)" εἰ δὲ πλείους, ἢ πεπερασμένας ἢ ἀπείρους" \, é my, δὲ lot Bi ὃ rg ” καὶ εἰ πεπερασμένας πλείους δὲ μιᾶς, ἢ δύο ἢ a Ἃ 4 aN ἴλλι Δ 3 θ ἕως \ ᾽ τρεῖς ἢ τέτταρας ἢ ἄλλον τινὰ ἀριθμόν: καὶ εἰ ἀπείρους, ἢ οὕτως ὥσπερ Δημόκριτος, τὸ γένος ἕν σχήματι δὲ ἢ εἴδει διαφερούσας, ἢ καὶ ἐναντίας. Opoiws δὲ ζητοῦσι καὶ of τὰ ὄντα ζητοῦντες πόσα' ἐξ ὧν γὰρ τὰ ὄντα ἐστί, πρῶτον ζητοῦσι ταῦτα πότερον ἕν ἢ πολλά, καὶ εἰ πολλά, πεπερα- A nm σμένα ἢ ἄπειρα" ὥστε THY ἀρχὴν καὶ τὸ στοιχεῖον ζητοῦσι πότερον ἕν ἢ πολλά, Τὸ μὲν οὖν εἰ ἐν καὶ ἀκίνητον τὸ ὃν σκοπεῖν οὐ περὶ φύσεώς ἐστι σκοπεῖν: ὥσπερ γὰρ καὶ τῷ γεωμέτρῃ οὐκέτι λόγος ἐστὶ πρὸς τὸν ἀνελόντα τὰς ἀρχάς, ἀλλ᾽ ἤτοι ἑτέρας ἐπιστήμης ἢ πασῶν κοινῆς, οὕτως οὐδὲ τῷ περὶ ἀρχῶν' οὐ γὰρ ἔτι ἀρχή ἐστιν, εἰ ἕν μόνον καὶ οὕτως ἕν ἐστιν" ἡ α ἢ καὶ ἐναντίας, not only ‘ differing in form,’ but also ‘of contrasted qualities’ (particles of bone, flesh, ete.) The reference, apparently, 1s to Anaxagoras. Cf. 1.1v, Ὁ. 43.
4 [For πρῶτον Bonitz conjectured πρώτων, 2.e, ‘ primary constituents.’ Similarly Plato (Soph. 242 c), after discussing Parmenides, reviews the other philosophers who have under- taken to decide the number and nature of τὰ ὄντα (ultimately real constituents of things): are they two or three, one or many, or both onc and many, ete.?—C.]
14 PHYSICS, I. 1.
Wert, then, there must be either one principle of Nature or more than one. And if only one, it must be either rigid, as Parmenides and Melissus say, or modifiable, as the Physicists say, some declaring air to be the first principle, and others water. If, on the other hand, there are more principles than one, they must be either limited or unlimited in number. And if limited, though more than one, they must be two or three or four, or some other definite number. And if they are unlimited, they must either be, as Democritus held, all of the same kind generically, though differing in shape and sub-characteristics, or of contrasted nature as well.2 The thinkers who inquire into the number of ‘ absolute entities,’ again, follow Lhe same line. For their first ὃ question is whether the constituents of which things are composed are one or more than one; and, if more than one, are they limited or unlimited? So they, too, are inquiring whether there is one principle or ultimate constituent, or many.
Now, as to the contention that all existence is one and is rigidly unchanging, we might say that it does not really concern the student of Nature, and he need not investigate it; any more than it concerns the geometer to argue with one who denies the geometrical axioms. Such questions must be dealt with either by some other special science or by a fundamental discipline that underlies all the sciences. And so it is in this matter of the unity of the naLural principle, for if it is only one, and one in the sense of rigidity. it is not a principle at all; for a principle must be the principle of some thing 15 ARISTOTLE 185a5 γὰρ ἀρχὴ τινὸς ἢ τινῶν. ὅμοιον δὴ τὸ σκοπεῖν εἰ οὕτως ἕν Kat πρὸς ἄλλην θέσιν ὁποιανοῦν δια- λέγεσθαι τῶν λόγου ἕνεκα λεγομένων (οἷον τὴν ¢ é an " ᾿ Mv 8 La A ay Ἡρακλείτειον, ἢ εἴ τις φαίη ἄνθρωπον ἕνα τὸ ὃν elvat) [ἢ λύειν λόγον ἐριστικόν, ὅπερ ἀμφότεροι μὲν ἔχουσιν of λόγοι, καὶ ὁ Μελίσσου καὶ ὁ 10 Παρμενίδου---καὶ γὰρ ψευδῆ λαμβάνουσι καὶ ἀσυλ- λόγιστοί εἰσιν---μᾶλλον δ᾽ 6 Μελίσσου φορτικὸς καὶ οὐκ ἔχων ἀπορίαν]. ἀλλ᾽ ἑνὸς ἀτόπου δοθέντος τὰ ἄλλα συμβαίνει: τοῦτο δὲ οὐδὲν χαλεπόν. ἡμῖν δ᾽ ὑποκείσθω τὰ φύσει ἢ πάντα ἢ ἔνια κινούμενα εἶναι" δῆλον δ᾽ ἐκ τῆς ἐπαγωγῆς. ἅμα δ᾽ οὐδὲ λύειν 1 o ἅπαντα προσήκει, GAN ἢ ὅσα ἐκ τῶν ἀρχῶν τις ἐπιδεικνὺς ψεύδεται, ὅσα δὲ μή, οὔ (οἷον τὸν τετραγωνισμὸν τὸν μὲν διὰ τῶν τμημάτων yew- μετρικοῦ διαλῦσαι, τὸν δ᾽ ᾿Αντιφῶντος οὐ yewpe- 1 (Bekker proposed to excise 8 ὅπερ ἀμφότεροι...12 χαλεπόν, comparing 186 a 6-10. W. bracketed ἢ λύειν λόγον ἐμιστικόν as ‘an editorial interpolation ’ and καὶ yap ψευδῆ...ἀπορίαν (sic) ‘ as a stray from 186 a7.’ But he must have meant to excise also ὅπερ ἀμφότεροι.. Παρμενίδου, which cannot stand alone and is not translated. 9 ἀλλ᾽ ἑνὸς, ᾿ς 12 χαλεπόν is bracketed at 18649. W.’s note is: ‘The whole of the passage which appears in Chapters II. and III. in the mss, and editions was regarded by Bekker, followed by Prantl, as belonging to the latter context. But if it is taken as a whole it contains a flat contradiction: ἀσυλλόγιστοί εἰσιν...GAN ἑνὸς ἀτόπου δοθέντος τᾶλλα συμβαίνει — “Their syllogisms are false...but their conclusions follow from their premises.” If the passage is divided between the two places, as I suggest, the contradiction 16 PHYSICS, I. 1.